Download Electric Potential

PHY294H
Professor: Joey Huston
email:[email protected]
office: BPS3230
Homework will be with Mastering Physics (and an average of 1 handwritten problem per week)
◆  Added problem 28.68 for 3rd MP assignment due Wed Feb. 3
as a hand-in problem
◆  Help-room hours: 12:40-2:40 Tues; 3:00-4:00 PM Friday
l  Quizzes by iclicker (sometimes hand-written)
l  Course website: www.pa.msu.edu/~huston/phy294h/index.html
◆  lectures will be posted frequently, mostly every day if I can
remember to do so
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!
!
A particle moving in an electric potential
The electric potential increases in the
! the E field.
direction opposite
!
Electric potential inside a parallel-plate capacitor
l  Go back again to a parallel
plate capacitor
◆  E = η/εo
◆ 
for the example given in the
book, E = 500 N/C
l  Inside the capacitor
◆ 
◆ 
◆ 
◆ 
V=Es, where s is the distance
from the negative plate
so potential increases linearly
with distance from the
negative plate
ΔVc = Ed = (500 N/C)(.003 m)
= 1.5 V
note: E=ΔVc/d
!
!
Electric potential inside a parallel-plate capacitor
l  E=ΔVc/d
◆  I can define the electric field
not in terms on the charges
creating it (the + and charges on the parallel
plates) but in terms of the
voltage between the plates
and their separation
l  Units for electric field
◆  before we used
▲  F=qE; E=F/q (N/C)
◆  now: E=ΔVc/d (V/m)
▲  1 N/C = 1 V/m
▲  can use either set of units
depending on which is
more convenient for the
problem at hand
!
!
Electric potential inside a parallel-plate capacitor
l  Note that I can write the
potential as
(d − x)
V = Es = ΔVc
d
x%
"
V = Es = $ 1 − ' ΔVc
#
d&
◆ 
voltage increases linearly
can draw equipotential lines
inside capacitor
!
!
Potential
l We have a potential
difference between
the two plates equal
to 1.5 V if we put a
charge density of
4.42 X 10-9 C/m2 on
each of the plates
l An easy way of doing
that is to connect a
1.5 V battery across
the two plates of the
capacitor
!
!
Arbitrariness of reference potential
!
!
iclicker question
A proton is released from
rest at the dot. Afterward,
the proton
A. 
Remains at the dot.
B.  Moves upward with steady speed.
C.  Moves upward with an increasing speed.
D.  Moves downward with a steady speed.
!
!
E.  Moves downward with an increasing speed.
iclicker question
A proton is released from
rest at the dot. Afterward,
the proton
A.  Remains at the dot.
B.  Moves upward with steady speed.
C.  Moves upward with an increasing speed.
D.  Moves downward with a steady speed.
!
!
E.  Moves downward with an increasing speed.
iclicker question
Two protons, one after the other,
are launched from point 1 with the
same speed. They follow the two
trajectories shown. The protons’
speeds at points 2 and 3 are related
by
A. 
B. 
C. 
D. 
v2 > v3.
v2 = v3.
v2 < v3.
Not enough information to compare their speeds.
!
!
iclicker question
Two protons, one after the other,
are launched from point 1 with the
same speed. They follow the two
trajectories shown. The protons’
speeds at points 2 and 3 are related
by
A.  v2 > v3.
B.  v2 = v3.
Energy conservation
C.  v2 < v3.
D.  Not enough information to compare their speeds.
!
!
Potential from a point charge
q
V=
4πε or
ActivPhysics Online
!
!
Potential from a charged sphere
l  What if I have a charged
sphere of radius R?
l  What does the potential
look like outside the
sphere (r>R)?
Q
1 Q
V=
4πε o r
l  At the surface,
1 Q
V=
4πε o R
R
r
What about inside the sphere? That !
depends on how
the charge is !
distributed.
Potential of many charges
l  If I have multiple charges,
then I have to calculate the
potential at any point from
each charge
1 qi
V =∑
i 4πε o ri
l  The electric potential, like the
electric field, obeys the
principle of superposition
l  Let’s consider an electric
dipole; we already know what
the electric field looks like
!
!
Potential of electric dipole
1 # q1 q 2 &
V=
+
4πε o %$ r1 r 2 ('
!
ActivPhysics
Online
!
At the midpoint between these two
equal but opposite charges,
A.  E = 0; V = 0.
B.  E = 0; V > 0.
C.  E = 0; V < 0.
D.  E points right; V = 0.
E.  E points left; V = 0.
!
!
At the midpoint between these two
equal but opposite charges,
A.  E = 0; V = 0.
B.  E = 0; V > 0.
C.  E = 0; V < 0.
D.  E points right; V = 0.
E.  E points left; V = 0.
!
!
Potential from continuous charge distributions
l  What if I have a
continuous charge
distribution?
l  Like the electric field for
a continuous charge
distribution, I
◆ 
◆ 
◆ 
divide the total charge Q
into many small point-like
charges ΔQ
use the knowledge of
potential of a point charge
to calculate the potential
from each ΔQ
calculate the total potential
by summing (integrating)
the potentials of all ΔQ
(dQ)
1
ΔQi
V=
∑
4πε o i ri
1
dq
V=
4πε!!o ∫ r
r
Potential from charged ring
…no integral to do
!
!
Potential from disk of charge
!
!
Another example before we leave this chapter
l  What is:
◆ 
◆ 
◆ 
◆ 
◆ 
the potential at points a
and b
the potential difference
between a and b
the potential energy of a
proton at a and b
the speed at point b of a
proton that was moving to
the right at point a with a
speed of 4 X 105 m/s
the speed at point a of a
proton that was moving to
the left at point b with a
speed of 5.3 X 105 m/s
1 nC
+
a
1 cm
3 cm
!
!
b